(i) a2+b2 = (2)2+(-2)2 = 4+4=8 [putting a=2,b=-2]
(ii) a2+ab+b2 = (2)2+(2)(-2)+(-2)2 = 4-4+4=4 [putting a=2,b=-2]
(iii)a2–b2 = (2)2-(-2)2 = 4-4=0 [putting a=2,b=-2]
If \( x, y \) are two positive integers such that \( x + y = 20 \) and the maximum value of \( x^3 y \) is \( k \) at \( x = a, y = \beta \), then \( \frac{k}{\alpha^2 \beta^2} = ? \)